As a paradigm for electron-based anomalous transport involving several fluctuating quantities, collisional drift wave turbulence is studied numerically in a sheared slab configuration. Nonlinear mode structure changes allow self-sustaining of the turbulence, even though no unstable linear modes exist. The responsible physics violates all the assumptions behind mixing-length, or turbulence-as-diffusion models, and so the turbulence is necessarily not of that type. The key ingredients are shared by all important transport candidates. Further, this single model displays several important properties known from tokamak transport-isotope mass trends, up-gradient transport ('inward pinch'), and ExB shear effects-which have lacking or dubious explanations within the existing framework. It can therefore serve as a useful basis for building new, and more realistic, scenarios for inhomogeneous turbulent transport.